Effective conductivity of a composite material with stiff imperfect contact conditions

We present an analytic and numerical analysis of several properties of a composite material with stiff imperfect interface conditions. Spaces of functions are identified wherewe can guarantee existence and uniqueness of solutions. In particular, formulas for the temperature distribution and flux are exhibited. Numerical calculations of the material characteristics such as temperature, flux and the effective conductivity are also performed and interpreted. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite amplitude long-wave instability of a thin viscoelastic fluid during spin coating

This paper investigates the stability of a thin incompressible viscoelastic fluid designated as Walters’ liquid B″ during spin coating. The long-wave perturbation method is proposed to derive a generalized kinematic model of the film flow. The method of normal mode is applied to study the linear stability. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. Using the multiple scales method, the weakly nonlinear stability analysis is studied for the evolution equation of a film flow. The Ginzburg–Landau equation is determined to discuss the threshold conditions of the various critical flow states. The study reveals that the rotation number and the radius of the rotating circular disk generate the destabilizing effects. Moreover, the viscoelastic parameter k indeed plays a more significant role in destabilizing the film flow than a thin Newtonian fluid during spin coating [27].     

Effect of surface modification of fibers with a polymer coating on the interlaminar shear strength of a composite and the translation of fiber strength in an F-12 aramid/epoxy composite vessel

The surface of aramid fibers was modified with a polymer coating — a surface treatment reagent containing epoxy resin. The resulting fibers were examined by using NOL tests, hydroburst tests, and the scanning electron microscopy. The modified fibers had a rougher surface than the untreated ones. The interlaminar shear strength of an aramid-fiber-reinforced epoxy composite was highest when the concentration of polymer coating system was 5%. The translation of fiber strength in an aramid/epoxy composite vessel was improved by 8%. The mechanism of the surface treatment of fibers in improving the mechanical properties of aramid/epoxy composites is discussed. Russian translation publeshed in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 729–738, November–December, 2006.     

Unfitted finite element methods for the heat conduction in composite media with contact resistance

This article is concerned with the heat conduction problem in composite media. In practical applications, the composite materials often do not contact well and there exist gaps between the contacting materials. This leads to the thermal contact resistance effect which results in a discontinuity of the temperature across the interface. In this article, an unfitted finite element method is proposed to solve the problem. Different from the traditional finite element method, the proposed method uses structured meshes that allow the interface to cut through. To avoid integrating on curved domains and interfaces, the interface is approximated by a broken line/plane corresponding to the triangulation. In addition, a ghost‐penalty is added to recover the condition number of the stiffness matrix to with a hidden constant independent of the mesh‐interface geometry. A rigorous analysis is provided. Finally, numerical tests are presented to verify the theoretical findings. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 354–380, 2017     

Analysis of contact stresses in structural joints of composite shell with steel banding

Based on the generalized Timoshenko-type shell theory, a numerical-analytical procedure for determining contact stresses from the interaction between a cylindrical composite shell and rigid bandings is proposed. Specific cases of loading and contact interaction (ideal contact through an adhesive interlayer) are considered. The contact problems are reduced to the solution of a Fredholm integral equation of the second-kind. A calculation analysis is performed. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 109–120, January–February, 2000.     

Buckling of stepped composite columns

The stability of elastic columns subjected to axial pressure is studied. An elastic multistepped column with rectangular cross sections are considered assuming that at the re-entrant corners of the column stable cracks are located. The influence of a crack on the loss of stability of the column is described by means of local flexibility and the function of compliance coupled with the stress intensity factor, which is known from the linear elastic fracture mechanics. A column with a single step is studied in more detail. The influence of crack location and length on the buckling load is assessed numerically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 87–100, January–February, 2006.     

Dynamics of elastic bodies connected by a thin soft viscoelastic layer

A dynamic study was performed on a structure consisting of two three-dimensional linearly elastic bodies connected by a thin soft nonlinear Kelvin–Voigt viscoelastic adhesive layer. The adhesive is assumed to be viscoelastic of Kelvin–Voigt generalized type, which makes it possible to deal with a relatively wide range of physical behavior by choosing suitable dissipation potentials. In the static and purely elastic case, convergence results when geometrical and mechanical parameters tend to zero have already been obtained using variational convergence methods. To obtain convergence results in the dynamic case, the main tool, as in the quasistatic case, is a nonlinear version of Trotter?s theory of approximation of semigroups acting on variable Hilbert spaces. The limit problem involves a mechanical constraint imposed along the surface to which the layer shrinks. The meaning of this limit with respect to the relative behavior of the parameters is discussed. The problem applies in particular to wave phenomena in bonded domains.     

Waer of composite thin-walled structural elements with consideration of thermal effects

The contact problem on interaction of rigid stamps with anisotropic plates with regard to wear and the corresponding frictional heating is considered. The procedure developed is based on the reduction of the governing equation to a system of Volterra integral equations of the second kind. The numerical analysis allows us to study the effects of both the anisotropic thermoelastic characteristics of materials and the nature of the interaction of the contact-pair elements on the wear process.Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 309–318, May–June, 1999.     

Braided reinforced composite rods for the internal reinforcement of concrete

This paper reports on the development of braided reinforced composite rods as a substitute for the steel reinforcement in concrete. The research work aims at understanding the mechanical behaviour of core-reinforced braided fabrics and braided reinforced composite rods, namely concerning the influence of the braiding angle, the type of core reinforcement fibre, and preloading and postloading conditions. The core-reinforced braided fabrics were made from polyester fibres for producing braided structures, and E-glass, carbon, HT polyethylene, and sisal fibres were used for the core reinforcement. The braided reinforced composite rods were obtained by impregnating the core-reinforced braided fabric with a vinyl ester resin. The preloading of the core-reinforced braided fabrics and the postloading of the braided reinforced composite rods were performed in three and two stages, respectively. The results of tensile tests carried out on different samples of core-reinforced braided fabrics are presented and discussed. The tensile and bending properties of the braided reinforced composite rods have been evaluated, and the results obtained are presented, discussed, and compared with those of conventional materials, such as steel. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 327–338, May–June, 2008.     

Solution of two-dimensional boundary-value problems of the theory of thin composite shells

Discrete analogues of the boundary-value problems of a two-dimensional refined theory of anisotropic shells taking into account the transverse shear deformation are presented. The systems of resolving equations in the general form are obtained for arbitrary nonshallow shells of variable curvature whose coordinate lines of the reduction surface may not coincide with the lines of principal curvatures. The algebraic problems of determining the stress-strain state in shells made of composite materials with stress concentrators under various kinds of loads are obtained as particular cases of the schemes presented. The results of calculating the stress concentration near a nonsmall circular hole in a transversely isotropic nonshallow spherical shell under internal pressure are presented. The dependences of stress concentration factors on the hole dimension and on a change in the shear stiffness of the shells are studied. A comparison between the calculation results obtained within the framework of the theories of shallow and nonshallow shells is given.Presented at the 11th International Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).Timoshenko Institute of Mechanics, Ukranian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 465–472, July–August, 2000.     

Method of primers in calculating the probability of destruction of a unidirectional composite material in tension

A method of primers is elaborated which allows one to calculate the distribution function of durability of a composite material in tension in the reinforcement direction. Integral and differential equations for calculating the probabilities of formation of primers and destruction of a material caused by their formation are presented. Distribution functions of material strength for the parameter of Weibull distribution of fiber strength on the interval 2.1 ≤ β _f ≤ 50.1 are calculated. From the functions, the average values and root-mean-square deviations of material strength are found. The results obtained agree well with calculations by using the structural-imitation simulation. The distribution functions of material strength with a high precision are approximated by the three-parameter Weibull distributions. The distribution parameters are approximated by the linear functions of ln (β_f). __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 823–838, November–December, 2007.     

Frictionless elliptical contact of thin viscoelastic layers bonded to rigid substrates

A three-dimensional unilateral contact problem for thin viscoelastic layers bonded to rigid substrates shaped like elliptic paraboloids is considered. Two cases are studied: (a) Poisson’s ratios of the layer materials are not very close to 0.5 and (b) the layer materials are incompressible with Poisson’s ratio of 0.5. Poisson’s ratios are assumed to be time independent. In the present paper we derive the general solutions to the problems of elliptical contact between thin compressible or incompressible layers of arbitrary viscoelastic materials. The approach is based on the analytical method developed by the authors for the elliptical contact of thin biphasic cartilage layers. The obtained analytical solution is valid for monotonically increasing loading conditions.     

Stress analysis for a rectangular thick plate of a composite material with a spatially locally curved structure under forced vibration

Natural and forced vibrations of a thick rectangular plate fabricated from a composite material with a spatially locally curved structure are investigated with the use of exact three-dimensional equations of motion of the theory of elastic anisotropic bodies. The investigations are carried out within the framework of the continuum approach developed by Akbarov and Guz. It is supposed that the plate is clamped at all its edges and is loaded on the upper face with uniformly distributed normal forces periodically changing with time. The influence of the parameters of local curving on the fundamental frequency of the plate and on the distribution of the normal stress acting in the thickness direction under forced vibration is studied. The corresponding boundary-value problems are solved numerically by employing the three-dimensional FEM modelling.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 779–790, November–December, 2004.     

小周期复合材料热传导问题的双尺度渐近展开及收敛性分析

利用双尺度渐近展开和均匀化思想讨论了小周期复合材料的热传导问题,得到了具有高阶震荡系数的抛物型方程的渐近展开式,并证明了当Ω为R~2中的光滑的区域时渐近展开式在空间L~2(0,T;H~1(Ω))中具有较好的收敛性.     

Asymptotic behavior of the second eigenfrequency for a system of two bodies connected by a thin rod

The method of matched asymptotic expansions is applied to the construction of the second eigenvalue, which tends to zero, in the problem corresponding to a system of two bodies connected by a thin rod.Institute of Mathematics, Urals Branch of the Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 1, pp. 68–77, October, 1993.     

Asymptotic analysis of 3D thin anisotropic plates with a piezoelectric patch

We consider a thin elastic plate with piezo patches mounted on top of it. Electrodes are located on the upper and, depending on the devices, at the lower surface of the patches. This piezo actuator is coupled to an elastic body. We develop an asymptotic procedure to derive a two‐dimensional approximation of the entire structure. As a result, we obtain an inhomogeneous fourth‐order plate equation with piecewise smooth coefficients for the vertical displacement coupled to a second‐order in‐plane problem. The analysis and the resulting asymptotic limits help clarifying the modeling issue concerning active piezo devices in multidimensional smart structures. Copyright © 2012 John Wiley & Sons, Ltd.     

球形涂层粒子增强复合材料的有效模量

本文通过四相球模型和复合材料的等效介质理论,研究了球形涂层粒子增强复合材料的有效模量性质,得到了这种增强复合材料的有效体积模量和有效剪切模量的理论预测公式。这些结果在特殊情况下,可退化到三相球模型确定的球形粒子增强复合材料的有效模量公式。     

Estimating the parameters of fatigue curve of a composite material

By using the method of maximum likelihood, the parameters of two versions of a mathematical model for fatigue damage accumulation in a laminate are estimated. The models, which are founded on the Markov chain theory, are very simple: they do not take into account the specific structural features of a composite and therefore cannot provide numerical coincidence with experimental fatigue test data, but they can be used for a nonlinear regression analysis of fatigue curves. A simple method is offered for approximately estimating model parameters, some of which characterize the distribution of the local static strength. By using such models, we can predict the relative changes in fatigue curves from known relative variations in the parameters of static strength and also predict the distribution function of fatigue life in program fatigue tests.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 109–120, January–February, 2005.     

Reinforcement of a thin plate by a thin layer

We study the bending of a thin plate, stiffened with a thin elastic layer, of thickness δ. We describe the complete construction of an asymptotic expansion with respect to δ of the solution of the Kirchhoff–Love model and give optimal estimates for the remainder. We identify approximate boundary conditions, which take into account the effect of the stiffener at various orders. Thanks to the tools of multi‐scale analysis, we give optimal estimates for the error between the approximate problems and the original one. We deal with a layer of constant stiffness, as well as with a stiffness in δ^?1. Copyright © 2007 John Wiley & Sons, Ltd.